Bleaching colors

I was just putting in a load of kitchen towels and put in some of the Color-Safe Bleach I bought last summer and have never used before.

And it just got me wondering: what exactly is color safe bleach? Isn't bleach supposed to make your whites whiter? If you're bleaching your colors, what exactly are you trying to achieve? Is it for things that are striped, and you need to get the white stripes white?